A different kind of lagged preconditioner

[Rafael Santos Coelho]

Hello everyone,

Lately I've been running some tests with a matrix-free LU-SGS-like
preconditioner and I've noticed that although, broadly speaking, it has
shown very good improvements on the convergence rate of my program, it does
not decrease the runtime. Quite the opposite, the bigger the problem (mesh
size), the more computational costlier it gets to be applied to the system,
which is fairly natural to expect. So I've tried using the
-snes_lag_preconditioner command-line option, and it did help in a way to
alleviate the "numerical effort" of the preconditioner, but the overall
runtime, in comparison with the matrix-free unpreconditioned tests, is still
prohibitive.

Given that, I was thinking of modifying the concept of "lagged
preconditioning" in PETSc, I mean, instead of applying the preconditioner
every "p" non-linear iterations, I want to apply it every "p" linear
iterations within each non-linear iteration. How can I do that?

Thanks in advance,

Rafael
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